A class of prime fusion categories of dimension 2^N
We study a class of strictly weakly integral fusion categories I_{N,ζ}, where N≥1 is a natural number and ζ is a 2^Nth root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2^{N+1} and is a graded extension of a pointed fusion category of ra...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/172764 |
| Acceso en línea: | http://hdl.handle.net/11336/172764 |
| Access Level: | acceso abierto |
| Palabra clave: | FUSION CATEGORY BRAIDES FUSION CATEGORY GROUP EXTENSION ISING CATEGORY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We study a class of strictly weakly integral fusion categories I_{N,ζ}, where N≥1 is a natural number and ζ is a 2^Nth root of unity, that we call N-Ising fusion categories. An N-Ising fusion category has Frobenius-Perron dimension 2^{N+1} and is a graded extension of a pointed fusion category of rank 2 by the cyclic group of order Z_{2^N}. We show that every braided N-Ising fusion category is prime and also that there exists a slightly degenerate N-Ising braided fusion category for all N>2. We also prove a structure result for braided extensions of a rank 2 pointed fusion category in terms of braided N-Ising fusion categories. |
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